Anistropic shader: mine doesn't converge at centre
It looks like your cylinder has been rotated in Edit Mode and its vertical axis isn't the Z axis anymore.

Fixing it is not straightforward. You should either rotate it back (still in Edit Mode) if you can tell which one would be the right rotation, or you should use custom transform orientations -- which are a bit of an overkill.

If the geometry isn't too complicated, I'd suggest starting this object over.